Primel Length Units
= Table of Primel Length Units = = The Primel Base Unit of Length: The ′lengthel, or ′morsel = The Primel base unit of length, the ′lengthel (abbreviated ′Lgℓ), is derived by taking the product of the ′velocitel and the ′timel (which in turn is derived by taking the product of the ′accelerel and the ′timel). :: ′lengthel = ′velocitel × ′timel = ′accelerel × ′timel2 This represents a distance traveled by an object moving at exactly 1.0204704d kilometers per hour over the course of 1 ′jiff, i.e., 50/1728d of a second (0.042z seconds). The resulting length is a bit smaller than a centimeter: It is exactly 8.202083d millimeters, or exactly 31/96d=0.322916d inch (exactly 27/80=0.3Ӿ6z inch). Primel proposes colloquializing this unit as the ′morsel-length. It also happens to be a very close approximation for the line spacing of standard ruled paper. In the US, wide-ruled/legal-ruled paper spaces its lines 11/32=0.34375 inch (Ɛ/28=0.416z inch) apart. US medium-ruled/college-ruled paper spaces its lines 9/32=0.28125 inch (9/28=0.376z inch) apart. The ′lengthel is almost directly intermediate between these. This means that any standard notebook makes a fairly good approximation of a Primel ruler. You could use it to get a rough idea of how ordinary objects would be measured. Consequently, Primel proposes ′spacing-length as an alternative colloquialism for this unit. For those accustomed to base units of length being at the scale of the USC foot or the SI meter, this may appear at first glance to be a rather small unit to serve as the basis for a system of measure. However, note that historically the centimeter itself actually served in such a role, as a foundation for the CGS (centimeter-gram-second) system, until that was supplanted by the MKS (meter-kilogram-second) system, now known as SI. The centimeter was, and still is, eminently serviceable as a unit of measure, and the ′lengthel is at least as serviceable. In fact, when we consider the ′lengthel together with its dozenal powers (as well as some simple multiples), they turn out to constitute a very useful suite of length units. = Positive Dozenal Powers of the ′Lengthel = The unqua′lengthel, or ′hand-length The first positive dozenal power of the ′lengthel, the unqua′lengthel (abbreviated u↑′Lgℓ) is a dozen ′morsel-lengths. This is the distance traversed in a ′twinkling (a little over a third of a second) when moving at 1 ′velocitel. In SI units, this comes out to exactly 9.8425d centimeters, and therefore is very close to 1 decimeter. In USC units, it comes out to exactly 31/8=3.875d inches (27/8=3.Ӿ6z inches). This makes a good approximation for the USC "hand" unit, which is 4 USC inches. As a consequence, Primel proposes nicknaming this the ′hand-length (or ′manipular-length). The biqua′lengthel, or ′ell-length The second dozenal power of the ′lengthel, the biqua′lengthel (abbreviated b↑′Lgℓ) is a dozen ′hand-lengths, or 100z ′morsel-lengths. This is the distance traversed in 1 ′lull (4.2z seconds) when moving at 1 ′velocitel. In SI units, this comes out to exactly 118.11d centimeters, very close to a dozen decimeters. In USC units, it comes out to exactly 46.5d (3Ӿ.6z) inches. This makes a good approximation for the English "ell", an old unit of cloth measure, which was 45d (39z) inches. Consequently, Primel proposes to colloquialize this the ′ell-length (or ′ulnaral-length). (The English word "ell" appears to be derived from the Latin ulna, "forearm", which would actually suggest a length half as large. However, clothiers evidently measured out cloth stretched across both forearms. Since the Latin genitive plural for ulna is ulnarum, "of the forearms", Primel derives the adjective "ulnaral" from that.) The triqua′lengthel, or ′habital-length Venturing beyond the "human-body" scale, the third dozenal power of the ′lengthel, the triqua′lengthel (abbreviated t↑′Lgℓ) is a dozen ′ell-lengths, or 100z ′hand-lengths, or 1000z ′morsel-lengths. This is the distance traversed in a ′trice (50d (42z) seconds) when moving at 1 ′velocitel. In SI units, this comes out to exactly 14.1732d meters. In USC units, this is exactly 46.5d (3Ӿ.6z) feet, or 15.5d (13.6z) yards. This is on the order of the size of a house. In fact, it turns out that a square with a side of this length would almost exactly correspond to the floor area of an average new home in the United States. Consequently, Primel proposes to colloquialize this the ′habital-length (or ′house-length). The quadqua′lengthel, or ′stadial-length The fourth dozenal power of the ′lengthel, the quadqua′lengthel (abbreviated q↑′Lgℓ) is a dozen ′habital-lengths, or 100z ′ell-lengths, or 1000z ′hand-lengths, or 10,000z ′morsel-lengths. This is the distance traversed in a ′breather (10d (Ӿz) minutes) when moving at 1 ′velocitel. In SI units, this comes out to exactly 170.0784d meters. In USC units, this is exactly 558d (3Ӿ6z) feet, or 186d (136z) yards. The nearest modern-day analog to this length that comes to mind is the furlong. However, at 660d (470z) feet, the furlong is a rather poor match: It comes out to about 1.22z quadqua′lengthels, more than a sixth too large; the quadqua′lengthel is only about 84.5%d (Ӿ1.9%z) of a furlong, almost a sixth too small. However, there is an ancient unit of measure that makes a rather better match: the Greek [http://en.wikipedia.org/wiki/Stadion_%28unit_of_length%29 stadion] (στάδιον), Latinized as stadium, and Anglicized as stade. Herodotus defined the stadion as being 600d (420z) feet. However, different ancient Greek city-states had different definitions of the foot. Two prominent ones were the standard Attic/Alexandrian foot of about 308d milimeters, which would place the stadion at about 185d meters; and the Olympic foot (from the city-state of Olympia) of about 294d milimeters, which would place the stadion at about 176d meters. The quadqua′lengthel comes to about 91.9%d (Ɛ0.5%z) of the Attic stadion, and to about 96.6%d (Ɛ7.2%z) of the Olympic stadion. On the strength of this correspondence, Primel will adapt the Latin form of this word, to make the ′stadial-length the colloquialization for the quadqua′lengthel. It still makes a good approximation for the size of most modern sports stadiums. The pentqua′lengthel, or ′dromal-length The fifth dozenal power of the ′lengthel, the pentqua′lengthel (abbreviated p↑′Lgℓ) is a dozen ′stadial-lengths, or 100z ′habital-lengths, or 1000z ′ell-lengths, or 10,000z ′hand-lengths, or 100,000z ′morsel-lengths. This is the distance traversed in 1 ′dwell (2 hours) when moving at 1 ′velocitel. In SI units, this comes out to exacty 2042.9408d meters, just slightly over 2 kilometers. In USC units, this is exactly 6696d (3Ӿ60z) feet. This makes the pentqua′lengthel a good unit for travel distances, on the order of the mile. However, at more than a quarter larger than a statute mile (exactly 1.2681d mi), calling the pentqua′lengthel some kind of "mile" would not be a good fit. (See below for a better mile analog.) The pentqua′lengthel is a new sort of unit that needs a new name coined for it. About 2 kilometers appears to have been a threshold distance for a "long race" in ancient Greece. For instance, the dolichus (δόλιχος) event in the ancient Olympics has been described by one source as being a dozen stades long, or about 2.2d kilometers (although most sources place it as being about a league, or 3 miles). The ancient Greek word for "race-course" or "running track" is dromos (δρόμος). Several modern words incorporate it: palindrome, prodromal, hippodrome, velodrome, aerodrome. In modern Greek dromos has evolved into a simpler and more generalized meaning of "road", in just about every sense that "road" has in English. That includes not only a simple ordinary street, but also a "road to" someplace, and even the metaphorical sense of one's "road" through life. The pentqua′lengthel is certainly quite serviceable as a unit for measuring travel distances "on the road". Consequently, Primel will adapt a Latinized form of this word, and colloquialize the pentqua′lengthel as the ′dromal-length. The hexqua′lengthel, or ′itineral-length The sixth dozenal power of the ′lengthel, the hexqua′lengthel (abbreviated h↑′Lgℓ) is a dozen ′dromal-lengths, or 100z ′stadial-lengths, or 1000z ′habital-lengths, or 10,000z ′ell-lengths, or 100,000z ′hand-lengths, or 1,000,000z ′morsel-lengths. This is the distance traversed in 1 day when moving at 1 ′velocitel. In SI units, this comes out to exacty 24.4912896d (about 20.5Ӿ8Ɛz) kilometers. In USC units, this is exactly 80,352d (3Ӿ,600z) feet or 15.218d (13.2750z) miles. This turns out to be a fair estimate of the distance a Roman legion could move in a day. In modern times, it also is about the threshold distance beyond which a commute to work by automobile is considered to be severely detrimental to one's quality of life (including apparently being linked to a greatly increased risk for obesity). The Latin word for "a day's march" was iter (genitive itineris). From this we get the modern English words "itinerant" (someone who travels about), and "itinerary" (a travel schedule). Since the hexqua′lengthel appears to be conceptually linked to the concept of "daily travel", Primel proposes to colloquialize it as the ′itineral-length. The septqua′lengthel, or ′regional-length The seventh dozenal power of the ′lengthel, the septqua′lengthel (abbreviated s↑′Lgℓ) is a dozen ′itineral-lengths, or 100z ′dromal-lengths, or 10,000,000z ′morsel-lengths. An object moving at 1 ′velocitel it would take a dozen days to travel this distance. In SI units, this comes out to exactly 293.8954752d (about 205.Ӿ8Ɛz) kilometers. In USC units, this is exactly 964,224 (3Ӿ6,000z) feet, or exactly 182.618d (132.7502z) miles. Since this is a good size for measuring regional distances, Primel proposes nicknaming this unit the ′regional-length. The octqua′lengthel, or ′continental-length The eighth dozenal power of the ′lengthel, the octqua′lengthel (abbreviated o↑′Lgℓ) is a dozen ′regional-lengths, or 100z ′itineral-lengths, or 1000z ′dromal-lengths, or 100,000,000z ′morsel-lengths. An object moving at 1 ′velocitel it would take a 100z days to travel this distance. In SI units, this comes out to exact 3526.7457024d (about 205Ӿ.8Ɛz) kilometers. In USC units, this is exactly 11,570,688d (3,Ӿ60,000z) feet, or exactly 2191.418d (1327.5027z) miles. Since this is a good size for measuring continental distances, Primel proposes nicknaming this unit the ′continental-length. The ennqua′lengthel, or ′orbital-length The ninth dozenal power of the ′lengthel, the ennqua′lengthel (abbreviated e↑′Lgℓ) is a dozen ′continental-lengths, or 100z regional-lengths, or 1000z ′itineral-lengths, or 10,000z ′dromal-lengths, or 1,000,000,000z ′morsel-lengths. An object moving at 1 ′velocitel it would take a 1000z days to travel this distance. In SI units, this comes out to about 42,320.9484288d (20,5Ӿ8.Ɛz) kilometers. In USC units, this is exactly 26,297.018d (13,275.0275z) miles. This is somewhat more than the circumference of the Earth. If drawn as a circle around the Earth's center of mass, it would correspond to an orbit at an altitude of about 368.1d (268.2z) kilometers, which is right in the middle of the Low Earth Orbit range. If plotted as the radius of a circle drawn around the Earth's center, it be just slightly larger than the geostationary orbit. Accordingly, Primel proposes to nickname this unit the ′orbital-length. = Correlation of Primel Length and Time Powers = In summary, the ′velocitel can now be equated to: 1 ′orbital-length per triquaday 1 ′continental-length per biquaday 1 ′regional-length per unquaday 1 ′itineral-length per day 1 ′dromal-length per ′dwell 1 ′stadial-length per ′breather 1 ′habital-length ′trice 1 ′ell-length per ′lull 1 ′hand-length per ′twinkling 1 ′morsel-length per ′jiff = Auxiliary Length Units = We can create an entire series of interesting auxiliary units that are all triples of the lengthel's various dozenal powers, as well as some additional multiples that are similarly noteworthy: The trina′lengthel, or ′thumb-length If the ′lengthel approximates a third of an inch, then naturally 3 ′lengthels make a fair approximation of the inch itself. We can introduce this as an auxiliary unit called the trina′lengthel (abbreviated t•′Lgℓ). In USC units, this comes out to exactly 31/32=0.96875d inch (27/28=0.Ɛ76z inch). In SI units, it comes out to exactly 2.460625d (about 2.563Ӿ63z) centimeters. This is quite close to the so-called "metric inch", defined as exactly 2.5d (2.6z) centimeters. That said, it would not be appropriate to nickname the trina′lengthel a "Primel inch". This is because the English word "inch" is derived from the Latin word uncia, which meant exactly the same thing it now does in SDN: "a twelfth-part"! The inch got that name because it is a twelfth part of the foot (Latin pes). But in Primel terms, the trina′lengthel is not an "uncia" of its base unit, it is 3 base units. However, many languages use their word for "thumb" to mean "inch". For instance, the Latin word for "thumb" is pollex, and the Romans used this word for the length unit as well. Consequently, Primel proposes colloquializing the trina′lengthel as the Primel ′thumb-length (or ′pollical-length). The trinaunqua′lengthel, or ′foot-length A length of a dozen ′thumb-lengths can be introduced as an auxiliary unit called the trinaunqua′lengthel (abbreviation t•u↑′Lgℓ). This is 3 ′hand-lengths, or 30z ′morsel-lengths. This makes a fair approximation of the USC foot, coming out to exacty 11.625d (Ɛ.76z) inches, or exactly 0.96875d (0.Ɛ76z) foot. In SI units, it comes out to exacty 29.5275d (about 25.63Ӿ63z) centimeters, which is quite close to 30d (26z) centimeters, also known as the "metric foot". Consequently, Primel proposes nicknaming this the ′foot-length (or ′podial-length). (Were it not for the difference between the TGM Gee and the Primel ′accelerel, the ′foot-length would be identical to the TGM Grafut.) The enneaunqua′lengthel, or ′yard-length Three ′foot-lengths, or 30z ′thumb-lengths, can be introduced as an auxiliary unit called the enneaunqua′lengthel (abbreviation e•u↑′Lgℓ). This is 9 ′hand-lengths, or 90z ′morsel-lengths. This makes a fair approximation of the USC yard, coming out to exactly 34.875d (2Ӿ.Ӿ6z) inches, or exactly 2.90625d (2.ӾӾ6z) feet, or exactly 0.968757d (0.Ɛ76z) yards. In SI units, it comes out to exactly 0.885825d (about 0.Ӿ76857z) meters, which is quite close to 90d (76z) centimeters, which is three "metric feet". Consequently, Primel proposes nicknaming this the ′brachial-length (or ′yard-length). The sesqui-biqua′lengthel, or ′fathom-length Two ′yard-lengths, or 6 ′foot-lengths, or 60z ′thumb-lengths, can be introduced as an auxiliary unit called the sesqui-biqua′lengthel (abbreviation ′u!h•b↑′Lgℓ). This is 160z ′morsels, or 16z ′hand-lengths, or one and a half ′ell-lengths (and hence could also be called a sesqui′ell-length). In SI units, this comes out to exactly 177.165d (about 129.1Ӿ9z) centimeters, or exacty 1.77165d (about 1.9314Ӿz) meters. In USC units, this is exactly 69.75d (59.9z inches), or exacty 5.8125d (5.99z) feet, or exacty 1.9375d (1.Ӿ3z) yards. This is a fair approximation of the nautical fathom, which is 6 USC feet. Consequently, Primel proposes to colloquialize this the ′fathom-length. It also happens to be very close to the average height for males in the United States. The trina-biqua′lengthel, or ′chambral-length (′room-length) A dozen ′foot-lengths, or 100z ′thumb-lengths, can be introduced as an auxiliary unit called the trina-biqua′lengthel (abbreviation t•b↑′Lgℓ). This is 3 ′ell-lengths, or 30z ′hand-lengths, or 300z ′morsel-lengths. In SI units, this comes out to exacty 3.5433d (about 3.6629Ӿz) meters. In USC units, this is exacty 139.5d (Ɛ7.6z) inches, or 11.625d (Ɛ.76z) feet. Since this is on the order of the size of a room in a house, Primel proposes to nickname this unit the ′chambral-length (or ′room-length). The trina-triqua′lengthel, or ′colossal-length A dozen ′chambral-lengths, or 100z ′foot-lengths, can be introduced as an auxiliary unit called the trina-triqua′lengthel (abbreviation t•t↑′Lgℓ). This is 3 ′habital-lengths, or 30z ′ell-lengths, or 300z ′hand-lengths, or 3000z ′morsel-lengths. In SI units, this comes out to exactly 42.5196d (about 36.629Ӿz) meters. This is equivalent to exactly 139.5d (Ɛ7.6z) USC feet. This is on the order of the size of colossal statutes such as the Statue of Liberty in New York Harbor (which Emma Lazarus dubbed "The New Colossus", in the poem by that name). It also approximates the original height of the Amphitheatrum Flavium in Rome, also known as the Coliseum, due to the colossal statue of Nero, of about the same height, said to have been housed there. Consequently, Primel proposes to colloquialize the trina-triqua′lengthel as the ′colossal-length. The trina-quadqua′lengthel, or ′turrial-length (′tower-length) A dozen ′colossal-lengths, or 1000z ′foot-lengths, can be introduced as an auxiliary unit called the trina-quadqua′lengthel (abbreviation t•q↑′Lgℓ). This is 3 ′stadial-lengths, or 300z ′ell-lengths, or 3000z ′hand-lengths, or 30,000z ′morsel-lengths, or a quarter of a ′dromal-length. In SI units, this comes out to exactly 510.2352d (about 366.29Ӿz) meters. This is equivalent to exactly 1674d (Ɛ76z) USC feet, or exactly 0.317045d (0.397Ӿ30z) statute miles. This is on the order of the height a skyscraper such as the Willis Tower in Chicago (formerly the Search Tower). Therefore, Primel proposes to colloquialize this as the ′turrial-length (or ′tower-length), from turis, Latin for "tower". The hexa-quadqua′lengthel, or ′kayish-length Two ′turrial-lengths, or 2000z ′foot-lengths, can be introduced as an auxiliary unit called the ′hexa-quadqua′lengthel (abbreviation h•q↑′Lgℓ). This is 6 ′stadial-lengths, or 600z ′ell-lengths, or 6000z ′hand-lengths, or 60,000z ′morsel-lengths, or half a ′dromal-length. In SI units this comes out to exactly 1020.4704d (about 710.579z) meters, just slightly over 1 kilometer. This suggests is calling this unit a ′kayish-length, after a common colloquialism for the kilometer. The ennea-quadqua′lengthel, or ′milish-length Three ′turrial-lengths, or 3000z ′foot-lengths, or 1000z ′yard-lengths, can be introduced as an auxiliary unit called the ennea-quadqua′lengthel (abbreviation e•q↑′Lgℓ). This is 9 ′stadial-lengths, or 900z ′ell-lengths, or 9000z ′hand-lengths, or 90,000z ′morsel-lengths, or three-quarters of a ′dromal-length. In SI units this comes out to exactly 1530.7056d (about Ӿ76.857z) meters, just slightly over a kilometer and a half. In USC units this length is exactly 5022d (2ӾӾ6z) feet, or exactly 0.951136d (0.Ɛ4Ɛ691z) statute miles. This a very close approximation of a customary mile (much closer than the ′dromal-length). On the strength of this, Primel proposes colloquializing this length as a ′milish-length. The trina-pentqua′lengthel, or ′parasangal-length A dozen ′turrial-lengths, or 10,000z ′foot-lengths, can be introduced as an auxiliary unit called the trina-pentqua′lengthel (abbreviation t•p↑′Lgℓ). This is 3 ′dromal-lengths, or 3000z ′ell-lengths, or 30,000z ′hand-lengths, or 300,000z ′morsel-lengths. In SI units, this comes out to exactly 6122.8224d (about 3662.9Ӿ5z) meters. This is equivalent to exactly 20,088d (Ɛ760z) USC feet, or exactly 3.8045d (3.97Ӿ30z) statute miles. Traditionally, 3 customary miles (statute or nautical) has been called a "league". The ′dromal-length is the Prime dozenal power closest to the customary mile, and therefore likely to be the preferred measure of travel distances in a Primel world, playing the role of a Primel "mile-analog". Since the trina-pentqua′lengthel is three ′dromal-lengths, one might be tempted to colloquialize this as a "Primel league." But just as the ′dromal-length is a bit too outsized to match the customary mile, so too the tri′dromal-length is a bit too large to match the customary league. (The ennea-quadqua′lengthel, or ′mile-length, makes a much closer "Primel mile", so the bidottri-pentqua′lengthel (230,000z ′lengthels) would make a better "Primel league." However, there is an ancient unit of measure that might fit the bill much better: the Persian parasang. The trouble is, Western scholars of Persian antiquity are all over the map in their assessment of exactly how long the parasang actually was. Herodotus quoted a figure of 30d (26z) ancient Greek stadia, which certainly gets it into the ballpark. But other sources have claimed it was closer to 40d (34z) stadia, or even longer. Certainly a length of 36d (30z) stadia is not out of the question. However, modern Persia has weighed in on this, and has officially established a standardized metric version of the parasang (in contemporary Farsi, a farsang), defined to be exactly 6 SI kilometers (or about 3.8d customary miles). Certainly if anyone can be trusted to provide a conclusive definition of what the ancient parasang must have been, modern Persians would be the experts! Six kilometers is an extraordinarily close match to the trina-pentqua′lengthel. On the strength of this, Primel proposes nicknaming this unit the ′parasangal-length. The trina-hexqua′lengthel, or ′provincial-length A dozen ′parasangal-lengths, or 100,000z ′foot-lengths, can be introduced as an auxiliary unit called the trina-hexqua′lengthel (abbreviation t•h↑′Lgℓ). This is 3 ′itineral-lengths, or 30,000z ′ell-lengths, or 300,000z ′hand-lengths, or 3,000,000z ′morsel-lengths. In SI units, this comes out to exactly 73,473.8688d (about 36,639.Ӿ51z) meters. This is equivalent to exactly 241,056d (Ɛ7,600z) USC feet, or exactly 45.654d (39.7Ӿ30z) statute miles. This is on the order of the size of a large county or small province or principality. Therefore, Primel proposes nicknaming this unit the ′provincial-length. The trina-septqua′lengthel, or ′territorial-length A dozen ′provincial-lengths, or 1,000,000z ′foot-lengths, can be introduced as an auxiliary unit called the trina-septqua′lengthel (abbreviation t•s↑′Lgℓ). This is 3 ′regional-lengths, or 300,000z ′ell-lengths, or 3,000,000z ′hand-lengths, or 30,000,000z ′morsel-lengths. In SI units, this comes out to exactly 881,686.4256d (about 366,39Ӿ.513z) meters. This is equivalent to exactly 2,892,672d (Ɛ76,000z) USC feet, or exactly 547.854d (397.Ӿ307z) statute miles. This is on the order of the territorial size of a moderate-sized nation. Therefore, Primel proposes nicknaming this unit the ′territorial-length. The trina-octqua′lengthel, or ′quadrantal-length A dozen ′territorial-lengths, or 10,000,000z ′foot-lengths, can be introduced as an auxiliary unit called the trina-octqua′lengthel (abbreviation t•o↑′Lgℓ). This is 3 ′continental-lengths, or 3,000,000z ′ell-lengths, or 30,000,000z ′hand-lengths, or 300,000,000z ′morsel-lengths. In SI units, this comes out to exactly 10,580,237.1072d (about 3,663,9Ӿ5.135z) meters. This is equivalent to exactly 34,712,064d (Ɛ,760,000z) USC feet, or exactly 6574.254d (397Ӿ.307Ӿz) statute miles. This is a quarter of ′orbital, so a bit larger than a quadrant of a great circle along the Earth, but equivalent to a quarter of a low-Earth orbit. Therefore, Primel proposes nicknaming this unit the ′quadrantal-length. = Table of Circumferal and Quadrantal Length Units = This is an auxiliary system of lengths useful for navigational purposes (analogous to nautical miles), based on using exactly 24,883.2d statute miles as a fair approximation of the circumference of the Earth. The © symbol can be pronounced "circum-", which hints at the fact that each of these units is "around about, but not quite" the size of a similarly-named Primel unit. So for instance, a ©dromal-length is about the size of a ′dromal-length. Each of these correlates with a similar fraction of a turn, as well as a similar fraction of the day, connecting this system with Earth's rotation and angular measures of latitude and longitude.